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L(R) absoluteness under proper forcings - MaRDI portal

L(R) absoluteness under proper forcings

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Publication:6501472

arXivmath/9909043MaRDI QIDQ6501472

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Abstract: We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and omega-Erdos cardinals. They are characterized by the existence of "0^sharp-like" embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(R) absoluteness under proper forcings. In particular, said absoluteness does not imply Pi^1_1 determinacy.





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